id	title	challengeType	forumTopicId	dashedName
5900f3d91000cf542c50feeb	Problem 108: Diophantine Reciprocals I	5	301732	problem-108-diophantine-reciprocals-i

--description--

In the following equation x, y, and n are positive integers.

1/x + 1/y = 1/n

For n = 4 there are exactly three distinct solutions:

1/5 + 1/20 = 1/4
1/6 + 1/12 = 1/4
1/8 + 1/8 = 1/4

What is the least value of n for which the number of distinct solutions exceeds one-thousand?

--hints--

diophantineOne() should return 180180.

assert.strictEqual(diophantineOne(), 180180);

function diophantineOne() {

  return true;
}

diophantineOne();

// solution required